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Finding the Third Proportional to 2,034 and 3,780

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Solution

The third proportional to 2,034 and 3,780 is: 7,024.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,034 : 3,780 = 3,780 : x
  2. Step 2: Convert to fraction form
    2,034/3,780 = 3,780/x
  3. Step 3: Cross multiply
    2,034x = 3,780 × 3,780
  4. Step 4: Simplify right side
    2,034x = 14,288,400
  5. Step 5: Solve for x
    x = 14,288,400/2,034
  6. Step 6: Final answer
    x = 7,024.78

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.